Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas*[email protected]. Caroline Jonas...

This paper discusses the state of the art of high-frequency trading (HFT), itsrequisite input, high-frequency data (HFD), and the impact of HFT on financialmarkets. The econometrics of HFD and trading marks a significant departurefrom the econometrics used when dealing with lower frequencies. In particular,ultra HFD might be randomly spaced, requiring point process techniques,while quantities such as volatility become nearly observable with HFD. Athigh frequency, forecasting opportunities that are different from those presentat lower frequencies appear, calling for new strategies and a new generationof trading algorithms. New risks associated with the speed of HFT emerge.The notion of interaction between algorithms becomes critical, requiring thecareful design of electronic markets.

In this paper, we discuss the state of the art of high-frequency trading (HFT) andimportant issues related to the econometric analysis of high-frequency data(HFD) and the impact of HFT on financial markets. The econometrics of HFDis different from standard econometric analysis employed in the analysis of lowerfrequency data. In particular, time series of HFD might be randomly spaced, therebyrequiring the techniques of point processes. Many quantities such as volatility becomenearly observable. At high frequency, forecasting opportunities that are differentfrom those present at lower frequency appear, calling for a new generation oftrading algorithms. As we explain in this paper, this results in the emergence of newrisks related to the speed of HFT. The notion of interaction between algorithmsbecomes critical, requiring the careful design of electronic markets.

*Frank J. Fabozzi CFA (the corresponding author) is a professor in the Practice of Finance at theYale School of Management. E-mail: [email protected] M. Focardi is a professor of finance at the EDHEC Business School. E-mail:[email protected] Jonas is a partner at The Intertek Group (Paris). E-mail: [email protected].

Acknowledgements: This survey paper on high-frequency data and high-frequency trading is basedon a review of the literature and conversations with 13 academics prominent in econometrics andmarket microstructure and three representatives from major exchanges. The academics have beenidentified throughout the paper; the exchange personnel whom we interviewed are not disclosed attheir request. The authors wish to thank all those who shared their insights and experience. Thispaper was prepared under a grant provided by The Institute for Financial Markets.

Keywords: high-frequency data (HFD), high-frequency trading (HFT)JEL Classification: G10, G12

Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas*

HIGH-FREQUENCY TRADING:METHODOLOGIES AND

MARKET IMPACT

Review of Futures Markets8

I. DEFINING HIGH-FREQUENCY TRADING

Although there is no universally accepted definition of HFT, among its definingcharacteristics are the fact that investments are held for very short periods of timeand typically (but not necessarily) positions are not carried overnight. How to quantifythese characteristics is a matter of debate. Kearns, Kulesza, and Nevmyvaka (2010)define high-frequency traders (HFTers) as those traders who hold positions between10 milliseconds and 10 seconds. However, the U.S. Securities and ExchangeCommission (SEC) adopts a somewhat less precise definition, defining HFTers asprofessionals acting in a proprietary capacity and able to generate a large numberof trades per day.

HFT is a form of trading that leverages high-speed computing, high-speedcommunications, tick-by-tick data, and technological advances to execute trades inas little as milliseconds. A typical objective of HFTers is to identify and capture(small) price discrepancies present in the market. They do so with no humanintervention, using computers to automatically capture and read market data inreal-time, transmit thousands of order messages per second to an exchange, andexecute, cancel, or replace orders based on new information on prices or demand.

High-speed trading strategies use computerized quantitative models (i.e.,algorithms) that identify which type of financial instrument (for example, stocks,options, or futures) to buy or sell, as well as the quantity, price, timing, and locationof the trades. In this paper, we focus on the equity market and equity futures andoptions. While algorithmic trading is now used in many asset classes, its origin is inequities and, still today, the share of trades based on algorithms is highest in theequity market (see Figure 1).

It is widely estimated that HFT was responsible for 40 to 70% of all tradingvolume in the U.S. equities market in 2009, roughly double its share just four yearsearlier; it is estimated to represent about 35 to 40% of all trading volume in Europeanequities.

In practice, HFT is engaged in by a wide variety of entities including proprietarydesks, hedge funds, and institutional investors. Nevertheless, it is estimated thathigh-frequency transactions in the U.S. equities markets are initiated by just 2% of

Figure 1. Algorithmic Trading Adoption by Asset Class.

Source: Aite Group estimates.

High-Frequency Trading 9

the 20,000 trading firms in the United States, that is to say, by some 400 firms (seeClark 2010). Many of these firms are privately held proprietary trading firms orhedge funds. The biggest players in HFT are reported to include the electronicmarket-makers Getco, Tradebot, Citadel, and QuantLab; hedge funds such as D.E.Shaw, SAC Global Advisors, and Renaissance Technologies; and the proprietarytrading desks of Goldman Sachs, Morgan Stanley, and Deutsche Bank. Thetechnology goal of HFTers is to reduce latency (i.e., delay) in placing, filling,confirming, or cancelling orders; the business goal is typically to profit from smallarbitrage opportunities present at short time horizons. Trading strategies differ andinclude electronic market-making and statistical arbitrage.

A. Setting the Stage for HFT

A number of factors have combined with technology to lead to an explosion in(algorithmic) trading activity. First, the 2001 decimalization of U.S. capital marketscoupled with smaller tick sizes led to an explosion in market data volumes.Chakravarty, Harris, and Wood (2001) analyzed the effect of decimalization in thetransition period and found a significant increase in trading volumes afterdecimalization. They note that the SEC expected a 139% increase in the number oftrades due to decimalization. Second, the cost of trading has dropped. This was aconsequence of several decisions, including the 1998 SEC decision to authorizeelectronic exchanges to compete with the traditional exchanges. It is estimated thatwhile in the 1990s the New York Stock Exchange (NYSE) and Nasdaq accountedfor 80% of trading volume in securities they listed, as much as 60 to 70% of tradingin their listed companies is now dispersed on as many as 50 competing tradingvenues, for the most part fully electronic. Third, an increase in derivatives productsand exchange-traded funds (ETFs) has led to an explosion in trading volumes.Angel, Harris, and Spatt (2010) report that equity trading volumes tripled in recentyears, going from about 3 billion shares per day in 2003 to nearly 10 billion sharesper day in 2009. According to data from the NYSE, average daily volume on U.S.stock exchanges was up 164 percent in 2009 compared to 2005 (see Duhigg 2009).

At the same time, high-performance computing systems, advanced tradingtechnology, and low-latency messaging middleware and feed handlers have reducedthe time necessary to execute market orders. Angel et al. (2010) cite data fromThomson, according to which the speed of execution for small market orders hasgone from about 25 seconds for NYSE-listed firms and 5 seconds for Nasdaq-listed firms in September 2001 to about 2.5 seconds in August 2009 (see Figure 2).

According to Eric Bertrand of NYSE Technologies (see Bertrand 2009), thecapacity as measured by order messages per day has gone from one million in 1995to hundreds of millions in 2009. During the same period (i.e., 1995–2009), throughputas measured by messages per second has gone from 20 to over 100,000 and latencyfrom one second to one thousandth of a second (i.e., one millisecond). At the sametime, network and data distribution speeds have gone from 64 kb per second to 10-100 Mb per second. Bertrand foresees order messages per day going to billions,messages per second to millions, latency to millionths of a second (i.e., microseconds),and network and data distribution speeds to a gigabyte per second.


To further reduce latency, HFTers are placing their trading servers at the tradingvenues to be close to the exchange matching engines. This is commonly referred toas co-location. In her March 2010 Chicago Fed Letter Carol Clark, a financialmarkets and payments system risk specialist in the Chicago Federal Reserve’sfinancial market group (see Clark 2010) remarks that it is estimated that for each100 miles the server is located away from the matching engine, 1 millisecond ofdelay is added to the time it takes to transmit trade instructions and execute matchedtrades or to access the central order book where information on buy/sell quotes andcurrent market prices is warehoused.

The NYSE is completing construction of a nearly 400,000-square-foot datacenter facility in Mahwah, New Jersey, where it hopes to attract in co-locationlarge Wall Street banks, traditional brokerages, and hedge funds. The center’s 40-gigabyte-per-second standard hardware will allow it to handle up to a millionmessages a second; new trading technology will reduce latency to 10 microseconds.Meanwhile, work is proceeding at the NYSE Euronext to design an ultra-low latencycore network that will support 50-microsecond roundtrips.

II. ECONOMETRICS FOR HFT AND ULTRA HFT DATA

As mentioned above, daily closing price data typically used in past efforts atmodeling financial markets are not sufficient for engineering HFT strategies; thelatter calls for the use of HFD, data taken at intraday frequencies, typically minutes.Data relative to each transaction, or tick-by-tick data, are called ultra high-frequencydata (UHFD). HFD and UHFD might be considered the fuel of HFT.

Note: Evolution of market order execution speeds as measured in seconds, concerning NYSE-listedand Nasdaq-listed firms during the period Sept 2001–August 2009 (from Angel et al., p. 22).Source: Rule 605 data from Thomson for all eligible market orders (100-9999 shares).

Figure 2. Market Order Execution Speed.


In this section we will first discuss questions related to the handling of (U)HFDand then discuss separately the modeling of HFD and UHFD. We will do so because,from an econometric perspective, there is a distinction between the methods andresearch objectives of HFD and UHFD. Both HFD and UHFD require econometricmethodologies different from those employed at lower frequencies.

A. Data Handling Issues

(U)HFD are routinely provided by electronic exchanges, albeit at a possiblyhigh price. Data currently available include tick-by-tick data and order-book data.A “tick” includes information at a given time, the “time stamp.” The sequence andcontent of the ticks might depend on the time of observations and on the exchangesthat are observed. Significant differences between the ticks of different exchangesmight be due to technology, exchange structure, and regulation. Order-book dataavailability is not the same on all exchanges. Some exchanges offer complete visibilityon the order book while others offer only partial visibility. Still other exchanges“flash” the order book only for a short period of time, for example, a fraction of asecond.

HFD and UHFD present significant problems of data handling. (See Brownleesand Gallo 2006 for a review of the challenges.) Both HFD and UHFD need to befiltered as errors and outliers might appear in a sequence of ticks. Bauwens andGiot (2001) and Oomen (2006), among others, deal with many aspects related todata cleansing. Brownlees and Gallo (2006) analyze the question of cleansing datafrom the NYSE’s Trades and Quotes (TAQ) files. Boehmer, Grammig, and Theissen(2006) discuss problems related to synchronizing data from the TAQ and from theNYSE’s order book.

Falkenberry (2002) reports that errors are present both in automatic andsemiautomatic trading systems. He reports that, as the speed of transactionsincreases, errors become more frequent. The first task in data cleansing is thereforethe elimination of erroneous data. However, it is also important to deal with outliersand with data that are not compatible with normal market activity. Methods foreliminating outliers are described in Boehmer et al. (2006).

In addition, HFD are not simply observed but imply some form of interpolationin order to represent prices. In fact, by the nature of the trading process, the truly“primitive” observations, that is, tick-by-tick data or UHFD, are an irregularly spacedtime series given that trading and quotes occur at random times. For example, thefrequency of UHFD for individual assets varies within a wide range of values infunction of the observed processes (i.e., trades). In his study of HFT activity relativeto 120 stocks traded on the NYSE, Brogaard (2010) found trading frequenciesranging from eight transactions per day for the lesser traded stocks to 60,000transactions per day, or roughly two transactions per second on average, for themost heavily traded stocks.

If we want to construct regularly spaced sequences of HFD, we must use amethodology to determine a price in moments when there are no transactions.Methods include linear interpolation between the two closest observations or using


the previous or ensuing observation. If data have a high frequency, these two methodsyield similar results. For rarely traded securities, different methods might result insignificant differences.

B. Better Econometrics with (U)HFD?

The availability of (U)FHD has been welcomed as a major advance with thepotential of revolutionizing the study and the practice of econometrics. Theexpectation is that with (U)HFD, market participants can significantly improve theestimation of parameters used in continuous-time finance and “observe” quantitiessuch as covariances or volatility as opposed to having to treat them as hiddenvariables.

However, it has become clear that there are significant limitations in the use ofHFD in general. As we will discuss, limitations come mainly from two sources.First, due to market microstructure effects, the behavior of prices at time horizonsof the order of seconds is different from the behavior of prices at time horizons ofminutes or longer, thus introducing basic limitations in the use of HFD. Second, it isdifficult to compute correlations and covariances between assets that trade atsignificantly different frequencies.

There are possibly different models at different time scales; a single modelthat is valid at every time scale and in every time window, if it exists at all, would betoo difficult to create and to estimate. The usual assumption is that prices follow ajump-diffusion process.

Jump-diffusion processes allow to describe with some accuracy the statisticaluncertainty of financial quantities. Thus, a jump-diffusion model of prices allows areasonable representation of the statistical characteristics of the uncertainty of thedistribution of returns and of co-movements between returns. However, thedeterministic drifts can be estimated only with limited precision, and they depend onthe data sample employed. Jump-diffusion processes do not allow one to makeaccurate forecasts based on trends and drifts. If we estimate jump-diffusionprocesses on different samples of past data, we obtain intrinsically different estimatesof drifts although the estimates of volatilities and covariances can be made reasonablycoherent. Therefore, although the use of HFD represents a significant step forwardin the estimation of some financial quantities, it does not allow us to formulateuniversal laws.

Let us now look at the limitations in the use of (U)HFD. From a purely statisticalpoint of view, estimates improve with a growing number of samples. Therefore, itwould seem reasonable to use all available (U)HFD. However the behavior ofprices at very high frequencies is not the same as the behavior of prices at lowerfrequencies. In fact, assuming that prices are modeled as jump-diffusion processes,as the length of sampling intervals approaches the length of trading intervals, microstructure effects introduce biases. These biases reduce the accuracy of forecasts.

Actually, as described in Aït-Sahalia and Mykland (2003), we can identifyseveral different effects that limit our ability to estimate continuous-time models.First, the inevitable discreteness of samples, both in time and price, introduces biases


in estimation. These are the first effects studied in the literature on estimatingcontinuous-time models. Second, the randomness of spacing, which introduces biasesthat, following Aït-Sahalia and Mykland, are at least as large as the discretenesseffects. Third, there are many microstructure effects, possibly exchange-dependent,which are generally accounted for as “noise” in the observation of prices. A numberof papers have analyzed the theoretical and empirical optimal sampling frequencyat which prices should be sampled to estimate the covariance matrix of diffusionprocesses.1

There is no consensus as to including noise in the observation of prices. IonutFlorescu, assistant professor of mathematics in the Department of MathematicalSciences of the Stevens Institute of Technology, remarks that the paradigm of noisyobservations is typical of physics and engineering, but he suggests that it does notreally apply to finance. Professor Florescu says, “A price of a trade is not a noisyobservation: We introduce noise only as a mathematical idealization.” His researcheffort is focused on estimating continuous-time models starting from “true”observations.

C. Using UHFD in Econometrics

The econometrics of UHFD is interested in representing the process of therandom arrival of trades. The latter is important to HFTers because there arerelationships between the volume of trades and prices. The econometric study ofUHFD cannot be performed with the usual methods of time series analysis, giventhat the latter assume observations at fixed time intervals. The problems associatedwith and methods applicable to UHFD are specific to randomly sampled data. Anearly model of nonsynchronous data is Lo and MacKinlay (1990). Bauwens andHautsch (2006a) and Hautsch (2004) provide overviews of the modeling of randomlyspaced financial data.

Trades are events of random magnitude that occur at random times. The timesat which trades take place are a sequence of strictly increasing random variables.The number of trades N(t) in any given interval is also a random variable. Processesof this type are referred to as point processes.

Point processes are continuous-time processes given that an event2 might occurat any moment; they are well known mathematical constructs in the field of insurancewhere claims of unpredictable magnitude occur at random times. The simplestpoint process is the Poisson process, which is characterized by the followingproperties:

• The number of events in any given interval of time is a random variable

that follows a Poisson distribution:

1. See, among others, Zhang, Mykland, and Aït-Sahalia, (2005), Aït-Sahalia, Mykland, and Zhang(2005), Bandi and Russell (2006), Bandi and Russell (2008), and Bandi, Russell, and Zhu (2008),Voev and Lunde (2007).2. We use the term “event” not in the sense of probabilistic events but to denote something thatoccurs at a given time, for example, a trade.

!ke

kλλ−


• The number of events in any given interval of time is independentfrom the number of events that occurred in any previous interval.

• The distribution of the time between two consecutive events followsan exponential distribution whose density is:

The parameter λ is called the intensity of the process. Poisson processes arecharacterized by constant intensity. The Poisson process is the point-processequivalent of the Brownian motion: It implements the notion of total uncertainty asregards the moment when the next event will occur. If a queue is described by aPoisson process, the probability that an event will occur in any future interval isunrelated to the time elapsed since the last event. For example, if a Poisson processdescribes the passage of a bus, a passenger waiting for the bus would have alwaysthe same probability to catch a bus in any next period independently of how long he/she has been waiting for the bus.

The Poisson process is a parsimoniously parameterized process with attractivemathematical properties, but it is too simple to describe the arrival times of trades.In fact, the time intervals between trades, referred to as the durations betweentrades, are not independent but exhibit autocorrelation phenomena. In order torepresent autocorrelations, we need to generalize Poisson processes to allow fortime-varying intensity. Point processes where the intensity is a separated processare called Cox processes.

Engle and Russell (1998) introduced a particular Cox process that they calledan Autoregressive Conditional Duration (ACD) process. ACD processes are thepoint process equivalent of ARCH/GARCH models insofar as they allowautoregressive intensity. The original ACD has been generalized and extended inmany different ways, for example in Bauwens and Veredas (2004) and Bauwensand Hautsch (2006b). McAleer and Medeiros (2008) and Pacurar (2008) provide asummary of theoretical and empirical work done on the ACD models. The ACDmodel and its generalizations are now widely used in the study of intra-trade durations.

D. The Econometric Study of HFD

While the econometrics of UHFD is mainly interested in representing the processof the random arrival of trades, the econometrics of HFD is principally interested inestimating covariances, which are fundamental data for any investment process.As described above, HFD are data taken at fixed intraday frequencies, typicallyfrom a few minutes to less than an hour. When raw data are prices in the form ofticks, HFD are recovered using some form of data aggregation and interpolation.

Although HFD are classical time series, they are typically modeled as continuous-time models, typically jump-diffusion processes, sampled at finite intervals. Theunderlying reasoning is that HFD tend to a continuous-time process if the observationfrequency grows. Intuitively, one might think that a jump is a large discontinuity sothat a jump-diffusion process simulates large movements such as crashes. However,mathematically this is not the case. A discontinuity is a point where the left and rightlimits of a path do not coincide regardless of the size of the difference. Therefore, a

te λλ −


jump-diffusion process is a rather abstract mathematical concept that is useful toprovide a better fit to the distribution of returns found empirically, but it is notnecessarily related to big jumps in price processes.

Mathematically, if we sample a continuous-time process with time intervalsthat tend to zero, many quantities estimated on the sampled process will tend to anaverage of the true parameters of the process. For example, if we compute acovariance matrix on a given interval using an increasing number of points, theempirical covariance matrix will tend to the average of the theoretical instantaneouscovariance. It should be noted that the above is a theoretical property of jump-diffusion processes sampled at frequencies that tend to infinity. Therefore, we canstate that volatilities and covariances estimated with high frequency intra-day datatend to the true volatilities and covariances only if we assume that price processesare jump-diffusion processes. If they are not, the above property might not hold.

1. Applying HFD to the Measurement of Volatility

With the above caveat, assuming prices are jump-diffusion processes, one ofthe major applications of HFD is the measurement of volatility. When prices andreturns are observed at time intervals of days or weeks, volatility is a hidden variabletypically modeled with ARCH/GARCH models. When HFD are available, volatilityis considered to be almost observable. This is because with HFD we have sufficientintraday data to estimate daily volatility as an average of the instantaneous volatility.Though it is conceptually wrong to say that volatility can be observed with HFD, itis nevertheless possible to make very precise estimates of the average volatilityover short intervals where volatility does not change much. A number of papershave discussed the measurement of volatility at high frequency.3

The problem of forecasting volatility remains. Because observed daily volatilitychanges significantly from day to day, there is the need to forecast volatility. Ageneral class of models for forecasting volatility, the Multiplicative Error Model,was introduced in Engle (2002) and extended in Cipollini, Engle, and Gallo (2006).For a comparison of different methods used to forecast volatility, see Brownleesand Gallo (2007).

From the above, it is clear that the interest in HFD is related to the fact thatthey make available a much larger quantity of data with respect to daily observations,and they do so without stretching the observation period. Dacorogna et al. (2001)observed that, on average, one day of HFD contains as many data as 30 years ofdaily data. Today, in some markets, this estimate can be multiplied 10 times. Therefore,it would seem reasonable to consider that HFD allow estimating richer models withmore parameters. However, this advantage might have limitations given that wehave to capture an intraday dynamics that is not needed when we model daily data.In other words, it is questionable if HFD aid us in understanding data at longer time

3. See, among others, Andersen, Bollerslev, Diebold and Labys, (2001), Andersen et al. (2003),Andersen, Bollerslev, and Meddahi (2002), Bandi and Phillips (2003), Barndorff-Nielsen and Shephard(2002a, b), Barndoff-Nielsen and Shephard (2004), Hansen, Lunde, and Voev (2007), and Ghysels,Santa-Clara, and Valkanov (2006).


horizons. For example, daily volatilities change and need to be forecasted; in additionvery short-term movements are generated by microstructure effects.

Commenting on how HFD can be used for forecasting longer time horizons,Ravi Jagannathan, Chicago Mercantile Exchange/John F. Sandner Professor ofFinance and a Co-Director of the Financial Institutions and Markets Research Centerat Northwestern University, remarks:

HFD does help forecast at longer time horizons, but not very long. HFDdo help for forecasting one week ahead, but not one year ahead. HFDposes an enormous challenge: If price moves between bid/ask,microstructure noise dominates. You need to filter out more microstructurenoise. For example, if you look at what happened 6 May 2010 and observeHFD, it will not tell you much about what might happen next week.

The question is primarily empirical, but there are also theoretical considerations.The problem can be stated as follows. Suppose there is a true price process p(t),which we assume is generated by a jump-diffusion mechanism. This model includesa time-dependent instantaneous covariance matrix pt . Suppose we can observe thetrue process only at discrete points pt in a given interval. It can be demonstrated(see Barndorff-Nielsen and Shephard 2002a,b) that if the frequency of observationstends to infinity, then the empirical covariance tends to the integral of the instantaneouscovariance.

However, if we assume that our observations are contaminated by marketmicrostructure noise, then estimates of the covariance matrix are negatively biased.Aït-Sahalia and Mykland (2003), Aït-Sahalia, Mykland, and Zhang (2005), Bandiand Russell (2006, 2008), Bandi, Russell, and Zhu (2008) determine the optimalsampling rate in the presence of microstructure effects.

Professor Jagannathan observes that, in the case of volatility measurements:

If markets are frictionless, that is, if there are no microstructure effects,the higher the frequency, the better the measurement of values as volatility.However, in rare or severe events, HFD are of no help; microstructure— the way people trade, the strategies used, lack of knowledge of whatthe others are doing — becomes more important. These effects areparticularly severe for illiquid stocks. To make use of HFD, you have tohave people trade at high frequency. If people trade at high frequency,you have observations. The econometrician can understand what is goingon.

E. Different Pricing Theories for Different Data Frequencies?

We observed above that there is a big difference in the frequency of trading atthe level of individual assets and that HFT has exacerbated this phenomenon in thatmost HFT is concentrated in a small number of stocks. Given this difference, andgiven the importance of HFD on pricing theories, we might ask if we need differentpricing theories for assets that are heavily traded and assets that are not. The


question can be reformulated as understanding what impact, if any, HFT has onprice processes.

Frederi Viens, Professor of Statistics and Mathematics and Director of theComputational Finance Program at Purdue University, offers an initial response:

It is my guess is that HFT impacts price processes in a big way. As far asI am aware, financial mathematics people have not yet found a way toexplain how to price equities under microstructure noise without arbitrage,and therefore I would venture to say that high-frequency-traded stockscan still be priced using standard frequency methods, but there will besome uncertainty in the pricing due to the microstructure noise. I am notaware of any way to perform equity and option pricing in an arbitrage-free way on UHFD without having to resort to saying that microstructurenoise exists. However, if one such way would exist, it would automaticallyimply that there should be two distinct pricing theories depending on thefrequency of trading. That would be a most uncomfortable situation. Myguess is that microstructure noise is real, so that we simply have to dealwith it, that is to say, account for the added uncertainty in our prices.Theoretically, this added uncertainly goes against the possibility of arbitrageopportunities. Since, in practice, the contrary is true, a balance will onlybe achieved when enough people have access to and the ability to workwith UHFD.

When discussing the relationship of HFD and long-term behavior, there areactually two distinct problems: the problem of the model itself and the problem ofnoise. Professor Viens observes:

The problem with HFD as it relates to longer-term trends is that themarket microstructure which is visible using HFD may or may not haveany bearing on the longer term trends. This is still being hotly debated inacademia. We are quite a way from being able to provide definite answerson this debate, and my guess is that the connection between the two willbe relevant in some markets, and irrelevant in others. … One theoreticalexample where the two are linked is the case of self-similar markets,particularly ones where stochastic long memory occurs because of so-called fractional Gaussian noise. From my experience with real data, Ican say that there is no evidence of any markets with such a self-similarityproperty. In other words, I have first-hand evidence showing that importantlong-term market parameters, such as stochastic long memory for volatilityseries, cannot be estimated using UHFD or even HFD.

F. Benefits of (U)HFD

In general, the more data that are available, the happier the statistician is. Foreconometricians and financial modelers, the availability of (U)HFD is beneficial tounderstanding what happens to prices intraday and might help shed light on financialeconometrics in general. Eric Ghysels, Bernstein Distinguished Professor of


Economics at the University of North Carolina’s Kenan-Flagler Business School,says:

HFD allow us to improve estimation of certain parameters or modelsused in various financial applications ranging from derivative pricing toasset allocation. HFD also allow us to improve upon existing market-based measures or to construct new ones. Prominent examples includevolatility and correlation. HFD and UHFD also allow us to study certainphenomena related to the actual trading process — topics that could notbe studied without such data. Examples here are abundant and relate tothe so-called market microstructure literature.

(U)HFD are also a challenge for the econometrician or modeler. NikolausHautsch, who holds the Chair of Econometrics at the Center for Applied Statisticsand Economics at Humboldt University in Berlin, comments:

HFD are affected by a lot of noise, lots of data with no information content.What matters is the ratio between the signal to noise. The signal-to-noiseratio must be greater than 1. If not, we have more noise than signal, andno gain. In the very beginning, the role of noise was overlooked. Over thepast four, five years, we have gained a better understanding of this.

We will now take a closer look at what academics to whom we spoke identifiedas specific benefits related to the availability and use of (U)HFD.

1. Better Understanding of Market Microstructure and the its Impact on Modeling

Academics we interviewed agreed that (U)HFD are useful in gaining anunderstanding of phenomena that occur intraday and the microstructure that causesthem. Chester Spatt, the Pamela R. and Kenneth B. Dunn Professor of Financeand Director of the Center for Financial Markets at Carnegie Mellon University’sDavid A. Tepper School of Business, comments:

There is information in small bids, small grains that might be significant asthey reflect opinions. But not all that shows up in trading is information; itmight be a question of micro market structure friction. (U)HFD is veryinteresting as it allows us to understand the trading process, to drill down.Using only daily data, one cannot understand the fundamentals of thetrading process, the motors of decision processes of traders in differentcontexts. For example, to what extent does an intermediary’s inventoryinfluence his decisions?

The expectation is that the availability of (U)HFD will allow better design ofexchanges. Valeri Voev, assistant professor of finance at the University of Aarhus(Denmark), says, “HFD is beneficial in studying the design of markets, to decide onmarket microstructure issues such as an order-driven or a quote-driven market, therole of specialists, etc., in an effort to design better markets.”

The analysis of HFD and the study of market microstructure go together, in


the sense that, while HFD reveal microstructure, it is also true that understandingmicrostructure offers a better understanding of HFD. As remarked by ProfessorGhysels:

The modeling of HFD is dependent on the exchange from which they aregenerated. Are there implications for price discovery and riskmanagement? This is a topic that has been widely studied in the marketmicrostructure literature, notably how price discovery takes place undervarious trading mechanisms. Part of this literature relies on the differenttime series characteristics of prices under alternative trading rules.

Professor Hautsch concurs, adding:

We definitely need to take into consideration the structure of the marketplace where the data is generated, for example, a market-maker orelectronic exchange. The dynamics are different, the levels of noise arequite different, the tick sizes are quite different. Some markets, for exampleelectronics markets, create a lot of noise. If one does not take thesefactors into consideration, one gets spurious results, strange outcomes.

Professor Florescu says, “(U)HFD offer an unparalleled opportunity to studythe trading process and implement learning with artificial intelligence as machinesare pitched one against the other and against humans.”

2. Improved Measurement of Phenomena at Lower Frequencies, Including Volatility,Covariance, and Risk

Academics whom we interviewed agreed that (U)HFD can also enhance anunderstanding of lower frequency phenomena, because (U)HFD allow one to modelobserved quantities and not only hidden quantities. Volatility is a case in point. Thoughwe need to forecast volatility, our forecasts are based on models of observed volatility.Luc Bauwens, professor of finance at the Catholic University in Louvain (Belgium),enumerates:

First, many useful theoretical pricing models are formulated in continuoustime. With UHFD especially, these models can be estimated much betterthan with less highly frequent data. Second, UHFD data allow to measurevolatilities of returns — say daily volatilities — much more precisely thanwithout these data — say when only daily data are available — through“realized volatilities.” Third, risk and liquidity can be measured in realtime with UHFD.

Professor Bauwens adds:

In all these areas, much progress is still to be made. From an econometricpoint of view, UHFD are interesting because they pose a number of issuesthat have not been much studied earlier by statisticians in the field offinance. There are many open questions in the analysis of time-dependent


data that are irregularly spaced and when the time dependences arecomplex, for instance, beyond the conditional mean.

According to Professor Voev:

We can benefit from HFD as many traditional markets use daily returns.Daily squared returns are very noisy. For example, if observations at thebeginning and end of the day are the same, then daily returns informationshows zero fluctuations versus if there were fluctuations during the day.We can get big performance gains if we use more frequent intraday databecause we obtain more statistical precision. We need to know the truevolatility ex post. With HFD can get very precise ex post measure ofvolatility. HFD are a good starting point to measure and understandvolatility.

However, just how to use HFD might not be so obvious. In fact, HFD permitthe precise measurement of past data but rely on forecasting to extrapolate thesemeasurements. Professor Voev comments, “Evidence is pretty clear that the HFDoffer better measurement but it is still not clear that we can optimize the use of thisinformation. When talking about multivariate data volatility, we need to come upwith models that allow forecasting matrices.”

However, estimating covariances between data at different frequencies is asignificant obstacle. According to Professor Hautsch:

Over the last 10 years, in the literature, the use of HFD has led to moreand more efficient estimates of the daily co-variance. However, thereare potential problems when we estimate quantities relative to data withdifferent frequency. Assets with high/low liquidity are a big problem ifone tries to correlate assets that trade thousands of times a day and assetsthat trade three times a day. This creates biases. It is a statistical problemthat needs to be resolved.

3. Improved Estimation of the Returns Distribution

Having thousands of observations of returns available, one can perform aprecise estimate of the return distribution. Of course, there is a caveat: If dailyreturns are required, we need to project high frequency returns onto daily returns.Doing so requires models of the time evolution of returns and precise measurementsof autocorrelations. Still, Professor Voev observes, “We obtain a much better designof the whole returns distribution based on thousands of trades per day.”

4. Better Understanding of Liquidity

The study of liquidity is a notoriously difficult problem. Its very definitionpresents difficulties. The availability of HFD, and more recently the diffusion ofHFT, allows one to shed more light on phenomena related to liquidity. ProfessorHautsch observes:


The relationship between liquidity and volatility is very difficult. We cannotunderstand it well from data 10 years or more back because liquidity thenplayed a completely different role from that it plays today. All work onmarket microstructure [when markets were populated by market-makers]is no longer relevant. We have a paradigm change, a fundamental changein markets.

5. Discovering New Facts

Professor Hautsch points to the role (U)HFD plays in discovering new factsand theories:

HFD are interesting in that they need new econometric models to takeinto account specific properties of data. Properties have changed quiterecently given the enormous liquidity in the markets. This raises newstatistical problems. The challenge is to manage higher dimensions ofdata: many characteristics, different markets, limit-order book data. HFDallow one to build better large-scale models, make better estimations ofcorrelations, better estimations of (high-dimensional) co-variance.

6. Improved Market Efficiency

Academics also agree that HFD (as well as HFT) has improved marketefficiency. Professor Viens comments:

From my standpoint as a mathematician and statistician working inquantitative finance with tools from stochastic analysis, I can only saythat the more HFD, and especially UHFD, become available to a wideraudience — including the ability to analyze such data thanks to increasingcomputational speed — the more efficient the market should become.

III. HIGH-FREQUENCY TRADING

HFT has become the subject of intense debate; it is feared that the use ofcomputerized programs and high-speed computers and communications networksthat characterize HFT might create new risks and allow HFTers to realize profitsat the expense of bona fide but less sophisticated investors.

Not everyone agrees. Bernard Donefer, Distinguished Lecturer in InformationTechnology in Financial Markets at Baruch College and Associate Director atSubotnick Financial Services Center, comments, “HFT itself is nothing more thanwhat has already been done, just off the exchange floor and faster.” Intuitively, onecan question if HFT is necessary for allocating capital efficiently to manufacturingor service firms whose investment process has long time horizons, often in therange of years. On the other hand, the econometrician’s view that financial priceprocesses are continuous-time processes can only welcome a development that


brings the reality of trading closer to the ideal of a continuous-time stochastic process.Clearly there are different views and different interests. While HFTers identify

and exploit profit opportunities and academics remark that market quality defined,for example, by the size of spreads, has improved, large institutional investors fearthat they are paying a tribute to HFTers for keeping markets efficient.

This has lead to the creation of “dark pools,” trading venues open only tospecific classes of investors, for example, large institutional investors, where memberscan trade anonymously and with the expectation that any market inefficiency willultimately profit themselves rather than being taken by intermediaries. Dark pools,estimated by sources to represent 7 to 8% of all U.S. equity trading, are themselvesopen to debate because of the lack of transparency.

In this section we will discuss the following issues:

• Is HFT a niche trading strategy or the future of equity markets?

• What phenomena do HFT strategies exploit to earn a profit?

• What is the impact of HFT on the price discovery process, on prices?

• What is the quality of the liquidity provided by HFT?

• What are the benefits of HFT?

• Does HFT introduce new risks?

• Is any new regulation needed to limit these risks?

• Who profits from HFT?

A. Niche Trading Strategy or the Future of Equity Markets

HFT, or the ability to exploit profit opportunities with trading strategiescharacterized by holding periods of a few minutes and without carrying positionsovernight, is a recent phenomenon. However, the market conditions enabling HFTwere created little more than a decade ago. As mentioned above, HFT was enabledby a combination of factors including the 2001 decimalization of U.S. equity markets,the advent of the electronic exchange, advances in computer and communicationstechnology, the availability of more data, and new modeling techniques. These factors,combined with the objective of large institutional investors to optimize the trading oflarge orders, led to algorithmic trading. Algorithmic trading is based on computerizedquantitative models and is used by large investors to reduce market impact. This istypically done by spreading large orders over many small transactions, therebycontributing to an increase in the volume of trading, a prerequisite for HFT.Algorithmic trading is not necessarily executed at high frequencies, but HFT isdependent on the development of algorithms. In addition, the ability to access directlythe electronic book at the exchanges created new trading opportunities.

A representative from a major options exchange in the United States comments:

The world of HFT would likely not exist in its present form if not for


decimalization which allowed for finer pricing. When the market tradedin 16ths, 8ths, spreads were very high; there was no capability to providea better market. Since decimalization, the bid-ask spread has been reduced.This led to a reduction of the overall cost of access to stock or optionprices. In the options market, this cost reduction has been multiplied thanksto penny stock trading.

Is HFT a niche market? The answer is two-pronged. On one side, HFTers area small highly specialized type of trader characterized by the use of advancedinformation technology and modeling techniques and short time horizons. On theother side, HFTers cannot exist in isolation: They need a robust flow of trades as amain source of profit. HFT, as well as other market participants such as hedgefunds, came into being to make a profit by exploiting regularities and inefficienciesin a flow of orders that already existed.

Different markets and different geographies have different populations ofHFTers. The share of trades executed by HFTers depends on how HFTers aredefined. It is widely accepted that in the U.S. equity market, HFT is responsible for40 to 70% of all trades. In a study based on tick-by-tick data from Nasdaq andadopting a widely used definition of HFT, Brogaard (2010) finds that, in 2009, wellabove 70% of all trades can be attributed to HFTs. One source at a U.S. optionsexchange observes:

Seventy percent is routinely accepted for market share of HFT in U.S.equity markets, but it depends on how you qualify participants. For example,market makers are intrinsically HFTers. In the equity options markets, Iwould put HFT market share at around 30 percent. Most HFTers in theoptions market tend to be very, very small because arbitrage opportunitiesare very small.

First developed in U.S. equity markets, HFT has now spread to other markets.The big players are present internationally, sources explained. However, HFTers’share of all trading in equity markets in Western Europe and Canada was estimatedto be anywhere from one third to one half their estimated share of the U.S. equitymarket. A representative from a major North American exchange remarks, “TheCanadian market has not been overwhelmed by HFT. I would estimate it to be 20–25 percent of all equity trading volume in Canada.”

We asked participants if, as short-term arbitrage opportunities are exploitedand disappear, HFT will also disappear. Professor Hautsch comments:

There will always be a need to have a certain level of HF strategies, HFTto ensure efficiency. As for opportunities for statistical arbitrage, I believethat we will see the introduction of new instruments, new assets, newtrading platforms. These will create micro arbitrage opportunities. It mightbe that in some markets, arbitrage opportunities will go to zero. But peoplewill keep on using HFT, if not for micro arbitrage, to exploit optimal tradeexecution.

The representative of a large North American exchange comments, “We expect


to see a blurring of lines between traditional players and HFTers as more traditionalplayers access HF technology.” We view this as blurring the lines between traditionalassets managers and “quants,” where the former have to some extent adoptedquantitative methods for at least some parts of their investment management process.

B. Phenomena HFT Strategies Exploit to Earn a Profit

An important question, both from the practical and academic points of view, iswhat type of strategies HFTers use. As strategies are proprietary, there is verylittle direct knowledge of strategies employed. We can only make general commentsand infer strategies from observing HFD. A first observation is that, given thespeed of trading, HFT strategies are based on information that changes rapidly.Therefore, it is unlikely that these strategies are based on fundamental informationon stocks or on macroeconomic data.

We can divide trading strategies at high frequency into three major categories.The first is based on trading on news, exploiting a time advantage in placing ordersbefore the market reacts to news. This involves automatic text reading and analysisand modeling techniques that relate news to price movements.

The second type of trading strategy is based on revealing small pricediscrepancies between different markets or between different assets that shouldtheoretically have the same price. Assuming that prices will realign rapidly, HFTersissue orders with low latency to exploit any arbitrage opportunity. This type ofstrategy is based on the ability to gather and analyze data, and then issue ordersvery rapidly before the market realigns. Exploiting arbitrage opportunities clearlyentails assessing the cost of the trade that is about to be made. If the cost of a tradeexceeds the size of the potential profit from arbitrage, then the trade is not executed.Wing Wah Tham, assistant professor of financial econometrics at the ErasmusSchool of Economics, observes, “Due to uncertainty in implementing trades, arbitragestrategies are not without risk even in the presence of arbitrage opportunities.”Kozham and Tham (2010) use HFD to study the role of execution risk due tocrowded trades in financial markets.

The third type of trading strategy is based on making short-term forecastsbased on the econometric properties of data. The most likely econometric propertiesto enter into a HFT strategy are prices, trading volumes, and information related topast trades. A special type of forecast is based on knowledge of the flow of incomingorders. In fact, the knowledge that large orders are coming is a type of informationthat traders have always exploited to their advantage.

Trading based on the knowledge that large orders are coming is called “frontrunning.” If and how this knowledge can be acquired is a subject of debate. In thelast 10 years, large long-term investors have invested in techniques to optimize theexecution of large orders. As discussed above, one such technique, algorithmictrading, allows one to split large orders into a flow of small orders, thereby matchinga flow of opposite orders and reducing market impact.

Secrecy is crucial to the success of algorithmic trading. If it is known in advancethat a large order flow is coming, the benefits of algorithmic trading are reduced.


Large investors therefore dislike methods and techniques that reveal their orderflow in advance. Barring any illegal disclosure of information, HFTers rely on issuingimmediate-or-cancel orders to search for and access all types of undisplayed liquidity,including liquidity in dark pools. They do so in the space of milliseconds. Thistechnique is called “pinging.” Whether or not pinging should be banned (or somehowrestricted) is now being debated.

In practice, strategies are implemented via trading rules that automaticallyissue orders when particular patterns of information are detected. While HFTersare often put into various categories, sources we interviewed remarked that thestrategies used by HFTers have evolved over the years. A representative from amajor North American exchange observes: “We see different strategies comingup. In the early stages, HFTers were mostly rebate takers, predatory. Now there isa more diverse range of strategies. Early adopters worked out inefficiencies inmarket; now there is the need for more effective strategies.”

The perception from academia is similar. Professor Hautsch remarks, “It ishard to observe different strategies from raw data, but from conversations withHFTers, it is clear that over the past three, four years, strategies have changeddramatically.”

Brogaard (2010) undertook a systematic exploration of HFT strategies basedon tick data from the Nasdaq for 120 stocks for the period 2008–2009. He findsthat most HFT strategies are based on short-term reversals. This opinion was sharedby sources from academia and the exchanges that we interviewed. A source at aNorth American exchange observes, “HFTers do not use long-term mean-revertingmodels; they are looking for arbitrage on intra-day mean reversion. They are differentfrom the market makers who take positions.”

While little is known about the trading strategies adopted by HFTers, we dohave information on a number of “stylized facts” about returns at very short timehorizons, in particular, on the probability distribution of orders and the autocorrelationof orders at very short time horizons (see, for example, Dacorogna et al. 2001).However, HFTers work on strategies typically tested over periods of at most twoyears. While the broad lines of trading strategies are known, the details areproprietary. It is likely that hundreds of technical HFT rules are used and continuouslyadapted.

C. Impact of HFT on the Price Discovery Process and on Prices

The question of the impact of HFD on the price discovery process and onprices is a multifaceted question that is not easy to define theoretically. This isbecause it requires a comparison of the actual outcome with some hypotheticaloutcome in the absence of HFT. Nevertheless, there is a consensus that HFTimpounds information faster and impacts some market parameters. Earlier studiesanalyzed the impact of decimalization on market quality (see, for example,Chakravarty et al. 2001 and Bessembinder 2003).

Terry Hendershott, at the Haas Finance Group at the University of California-Berkeley, observes, “If you consider the actual price as having fundamental


information plus noise, HFD has no long-term fundamental information, but HFTcan help get short-term information into prices faster.”

Brogaard (2010) analyzes the impact of HFT on market parameters such asvolatility and the bid-ask spread. He employs the now widely used methodology foranalyzing market quality introduced in Hasbrouck (1993). In the sample that heanalyzed (HFD from Nasdaq on 120 stocks for the period 2008–2009), he concludesthat volatility did not increase and the bid-ask spread was reduced. On these points,there seems to be agreement. HFTers have not produced an increase in volatility,as many had feared, and have generally had a beneficial effect on parameters thatdefine market quality such as the bid-ask spread.

One problem in analyzing the impact of HFT on the bid-ask spread is to separatethe impact of HFT and that of decimalization and other changes introduced in theU.S. equity markets over the last decade and a half. An industry source, whoconfirms having seen a reduction in the bid-ask spread due to the activity of HFTers,remarks:

If you look at the Canadian equity market, it’s easier to separate theimpact of HFT from that of decimalization. Decimalization was introducedin Canada in 1996 while HFT in Canada is relatively new, having startedonly as of late 2008–2009. It is possible to see a tightening of the spreadsthat occurred at the different time periods.

If we measure price efficiency in terms of parameters such as bid-ask spread,HFT has increased market efficiency. However, as HFTers trade against eachother using algorithms that are in general based on technical rules that have nothingto do with fundamentals, we can ask if HFT might cause prices to depart fromfundamentals. James MacIntosh, investment editor of the Financial Times, remarksthat fundamental information is no longer reflected in stock pricing (see MackIntosh2010). He suggests that pricing is now driven by market sentiment and possibly bythe increase in trading on trends and patterns.

One market fact that can possibly be ascribed to HFT is the observed increasein correlation. Professor Voev comments:

There is recent evidence that HFT is leading to more correlation, a factthat has serious implications for diversification. This is making it moredifficult to diversify with index tracking or exchange-traded funds. Thereare now thousands of algos trading indexes, moving prices. Is pricemomentum dominated by traders trading indexes?

Professor Bauwens comments that while HFT has improved market efficiencyoverall, there is the possibility that it can cause artificial price trends:

Finance theory holds that prices reflect past information but is not preciseon how this works. My conjecture is that HFT has in most cases increasedthe speed at at which prices adjust to reflect new information; thus, it hasled to increased efficiency. However, it has also been noted that correlationbetween intraday returns of stocks has increased without apparently much


reason, and this may be caused by HFT driven by econometric modelsdisconnected from fundamentals.

The action of HFTers has probably reduced volatility. Nevertheless, somesources mentioned that while volatility is down in normal times, HFT might lead tovolatility spikes. Professor Voev remarks:

We now have faster channels of market fear, uncertainty. Is HFT causingthis or is it just a question of faster channels, with HFT facilitating fastchanneling of emotions, fear? In normal times, HFT brings smootheradjustment to new levels versus discrete moves which are more volatile.But in more extreme circumstances, it can lead to spikes in volatility.

Commenting on the impact of HFT activity on volatility, an industry sourcesays, “It (is) hard for us as an exchange to evaluate the impact of HFT on markets.HFT has probably had a dampening effect on volatility as the bid-ask spread isconstantly narrowing except when all the HTFers turn off their computers. HFTersdon’t try to make their models fit beyond mean returns.”

D. More (or Better) Liquidity with HFT?

It is widely held that HFT provides liquidity to equity markets. However, HFTper se provides liquidity only for a very short time. By the nature of their business,HFTers buy and sell at high frequency. If they do not find a counterparty for a tradein a matter of seconds, orders are cancelled. These are the (in)famous flash trades.Among the academics and industry players we interviewed, opinions were dividedas to the nature of liquidity provided by HFTers. Some argue that liquidity providedby HFT is exercisable liquidity; those who question the benefit of HFT liquiditypoint to its fleeting quality.

Among those defending the utility of the short-term liquidity provided by HFT,the representative of a major North American exchange asks, “Is the liquidity providedby HFT real or phantom? It is tough to answer this given the different strategiesemployed by HFTers, but it is exercisable liquidity, available for someone to hit,even if it is only there for a short period. Certainly it is real if you have the technologyto grab it.”

Another industry source took the opposite position, arguing:

HFT does add liquidity on a very shallow basis on narrow prices for smallamounts and for pure retail customers. It is like a discount store that sellshandbags at a low price but has only one handbag around to sell. HFT isless a provider of liquidity for larger volumes. Liquidity provided by HFTersis not deep enough, it is fleeting.

Professor Spatt suggests that the nature of today’s liquidity is a reflection ofchanges in trading behavior. He comments:

The question of traders showing their hands versus HFTers coming outfor brief periods of time is the question of how to engage to obtain liquidity.


The types of tactics used by HFTers leads to cancellation rates that keepexploding. Most orders are now cancelled almost instantaneously. It isnot a question of being manipulative; HFTers are just trying to understandthe liquidity out there and scale up and trade against it. HFTers (are) alsolooking for a lack of liquidity. Liquidity provided by HFTers is not anillusion, but it is different from the usual liquidity. The old notion was thattraders want everyone else to show their hands without showing theirown hand but it does not work that way. You cannot mandate liquidity.You must make it attractive for people to show their hands without thefear of being picked off. If a trader shows impatience, he or she will notget a good price.

E. Do Markets Benefit from HFT?

We discussed above several widely ascribed, but not universally acclaimed,benefits of HFT to equity markets (i.e., a lowering of the bid-ask spreads, reducedvolatility, and increased albeit short-term liquidity). However, not everyone agrees.Professor Jagannathan suggests that the benefits of HFT have perhaps not beensufficiently or correctly studied:

The relative benefit if all trading once at the end of day as opposed toHFT has not been established. When people say markets are better offbecause of HFT, no one has correctly measured this against benefit oftrading at a lower frequency. Think about it. Suppose I know that somethingis happening and trade. My trade will affect the price at a point in time.Does it really matter if I know the price at exactly the minute rather thanat the end of the day? At the fundamental level, HFT will not make usmuch better off.

Angel et al. (2010) perform a detailed analysis of changes in equity tradingover the last 10 years. They conclude that the market quality has improved. ButJames Angel, co-author of the study and associate professor of finance atGeorgetown University’s McDonough School of Business, questions if pushing tradingever faster produces a real benefit:

Market-makers buy on a dip and sell on a rebound. They have made iteasier for the long-term investor to trade at lower costs. Cost reductionswere realized as computers replaced humans as market-makers. No onewould say that pure market-makers have hurt the investor. But how muchbenefit is there if pricing is made more accurate in seconds as opposed toin minutes? It is debatable.

Professor Spatt comments that the current environment has promoted morecompetition in the equity markets and that the competition has been beneficial. Buthe suggests that there is not enough competition in other markets. In particular, heobserves that there is inadequate attention on the bond market microstructure.

One benefit that the equity exchanges have seen is increased attention being


paid to listed firms, at least the larger of the listed firms. A representative from amajor North American exchange remarks:

The net benefit is that we have a better market with the participation ofHFTers. HFTers’ entry into the Canadian market led to an influx of newparticipants in the exchange. As a result there is a diversification of theorder flow and of trading strategies. Previously, in Canada, there was aconcentration of market participants. A knock-on effect is that, as bignames in the U.S. set their sights on Canada, others opened their eyesand began to look at the Canadian market. As liquidity improves, as tradingvelocity grows, the increased activity on listed shares means that firmsthat were before screened out by filters that screen out stocks that tradeless than 1 million shares a day are now traded. There is a benefit for thefirms as this gives them greater access to capital, lowers the cost ofcapital. What happens on an intraday basis does not have a material impacton the long-term investor if not when the investor wants to get into themarket. And when the long-term investor wants to get into the market,he/she finds a buyer/seller. Speculators facilitate the trade; they are anecessary element of the market place.

It might be, however, that the activity of HFTers is keeping some investorsaway from the equity markets. Spicer (2010) refers to data released in the beginningof September 2010 that show that flows have exited U.S. mutual fund accounts inevery week since the May 6th flash crash. He writes that these outflows are fuelingspeculation that the crash continues to undermine investor confidence. Fabozzi,Focardi, and Jonas (2010) remark that following the 2007–2009 market turmoil,regaining investor confidence is the biggest challenge for all in the financial servicesindustry. Retail investors have seen strong market movements without anyfundamental reason for the ups and downs. According to sources for that study,such movements are reinforcing people’s perception that markets are casinos andan inappropriate placement for one’s savings.

Nevertheless, Professor Jagannathan believes that, if market participants areuneasy about trading in venues where HFTers are active, they can trade elsewhere:“HFTers can trade among themselves and this might keep investors away. Peoplecould invent other markets, for example, you could have one auction a week muchas the old Dutch auction system. If the activity of HFTers gets really bad, peoplewill invent other things such as dark pools; it is an easy thing to fix.”

F. Does HFT Introduce New Market Risks?

Generally speaking, there is little understanding of the highly secretive strategiesused by HFTers. A representative of a U.S. options exchange comments:

If a HFTer does pure arbitrage and is not predatory, not manipulative,there is no problem. The problem is that we do not know. The SEC is nowrequesting all exchanges to identify HFTers by some formula, for example,


more than 399 trades/day and to tag trades for analysis. From theexchange’s standpoint, it is not possible to tell what the trader is doing ashe/she might be doing something in other markets, exchanges. It is hardto tell an elephant from touching one part of the body.

One problem is that data that have been collected by the regulators have nothelped to elucidate trading practices. Professor Donefer notes:

The problem is that regulators have been running at their studies on players,for example, broker-dealers, hedge funds, etc. FINRA [the largestindependent securities regulator in the U.S.] has no clue as to the kind oftrading being done and the strategies behind it. Regulators should requiretagging of orders by algos as opposed to by category of players.

To our knowledge, academic studies have not revealed any evidence of dubiouspractices by HFTers such as “front running,” a strategy based on anticipating thearrival of large orders. The (probabilistic) knowledge of the arrival of large ordersis in itself obtained through other practices such as “pinging,” which consists ofissuing and cancelling orders in the space of a few milliseconds in order to revealpools of existing liquidity. Nor, to our knowledge, have academic studies producedevidence of market manipulation.

Addressing the question of new risks introduced by HTF, Professor Hendershottremarks:

I am not sure that we have any evidence so far of new risks, but that doesnot mean it could not happen. Is the fear that algos create prices causingpeople to not understand what is the correct price in the market, eitherintentionally or unintentionally? If someone is causing prices to move in away as to not reflect information, others can trade against them and makemoney.

On the other hand, sources agreed that new risks related to technology andspeed have been introduced. Professor Angel remarks, “The high-speed world mightproduce some high-speed risks.” HFT can ultimately be described as fast machinestrading against other fast machines. Professor Angel adds:

I do not think HFT makes it easier to manipulate the market. Games tomanipulate the markets have been going on for 400 years. If anything, itis now harder to manipulate the market. But the big problem is marketsact so quickly now. Can something go wrong? Yes, consider, for exampleMay 6 (2010). There are various risks, such as run-away algos, computerfailures, intentional hacking, programming problems. Yes, the system isvulnerable to breakdown, to attack. So you need to have something inplace to respond as quickly as possible when computers crash, for example,circuit breakers, for when machines malfunction.

Persons we interviewed believe that the biggest problem with HFT is thepossibility of cascading effects (not the creation of bubbles) or system collapse due


to the high speed of trading or an excessive number of messages. Professor Donefer,who developed his argument in an article recently published in The Journal ofTrading (2010), remarks:

HFT and direct market access represent an additional risk in that allstrategies that track markets are pegged to NBBOs. Imagine that onealgo goes wild. All other markets see this, reset their prices, and there isa cascading effect. There are too many models based on the sameinformation, too many crowded trades.

Relative to cascading effects, Professor Voev comments:

When you have computers programmed to trade on price patterns, youmight have avalanche effects. Automatic trading can push prices waytoo low. If markets are efficient, the price bounces back to fundamentalvalues. But in some cases prices do not bounce back because there isgeneral market uncertainty and no one knows what the price should be.

In this sense, protecting the system is more a question of intelligent design oftrading than the issuing of rules banning this or that process. Referring to the use ofrule-based trading algorithms, Professor Jagannathan comments: “Anything that ismechanical, rule-based, needs oversight rules. Things change as you go along —portfolio insurance, the May 6 flash crash — and you need intelligent rules fortrading. If there is a large change in the price, rules should be in place to handlesuch situations.”

Sources pointed to the flash crash of May 6, 2010, when the Dow JonesIndustrial Average lost some 700 points before sharply rebounding in the space ofjust 20 minutes, to argue that the presence of HFTers likely helped the marketsbounce back rapidly. Professor Donefer remarks:

If you look at the flash crash of October 1987, there were market-makersbut people walked off the floor, and those that did not risked bankruptcy.Greenspan was just in as head of the Federal Reserve, and ordered thebanks to lend money to market-makers to keep them solvent, to help themarkets recover. It took one year for markets to recover from that crash.With the flash crash of May 6th and the presence of statistical arbitrageurs,HFTers, the market recovered in matter of less than one day as thesepeople got back into the market. When markets start to crash, risk modelstake over if the firm’s jeopardy is at stake. These firms are no longer thefamily businesses such as those in the 1987 crash, but corporations. Theyuse more sophisticated risk models. If they see too much capital at risk,they walk away from the markets. But they come back minutes laterwhen profit opportunities are identified. I have no first-hand knowledgeof what happened but my perception is that among the players in the May6th flash crash, there were high-frequency market-makers as Getco, Virtu,and Knight Capital. They all came back into the market right away.


In addition to the risk of cascading effects or technology-related risks due tothe speed and messaging typical of HFT activity, sources identified other risks suchas increased correlation. Professor Hautsch observes, “HFTers try to exploitstatistical arbitrage. This leads to greater correlations across markets, assets,instruments. In turn, diversification effects are weakened, leading to increased risk.Greater efficiency is a good thing but more correlation is a risk: Many nice portfoliomodels don’t work anymore.”

G. Is New Regulation Needed to Limit These Risks?

Though sources agreed that HFT has introduced new risks related to technology,there was no consensus as to how exchanges or regulators should respond. Somesources were in favor turning off the quant models and keeping only the market-makers or end buyers/sellers going; others suggested the use of circuit breakers.Commenting after the May 6th flash crash and the regulators’ move to bust tradeswhen prices moved far from their value, Professor Angel remarks, “Markets canget into situations, chaotic events in which an algo can push a price far from itsvalue. I favor circuit breakers and then switching to a different market mechanism,shutting all computers as is done at the Deutsche Boerse and then starting all overthe morning after with an auction.”

However, not all our interviewees were in favor of circuit breakers. ProfessorSpatt argues against circuit breakers as they are disruptive of the trading processbut is in favor of filters to catch mistakes. Professor Spatt is concerned about therisks created by intervention:

May 6th was a fiasco but one risk now created is that liquidity won’tarrive because of a lack of clarity in the process given the regulator’sdecision to cancel trades whose price movement was more than 60%while trades whose price movement was under 60% were not canceled.People are not under an obligation to keep providing liquidity and will pullback if they don’t understand what the regulator’s response to a situationwill be.

On October 1, 2010, the SEC released its report on the May 6th flash crash.The report attributes the crash to a cascade effect following an unusually largetrade ($4.1 billion). Two observations can be made.

1. It has been well established that intraday returns are fat-tailed, as arethe size of trades and indeed the capitalization of firms. In consequence,one should expect fat-tailed returns even in the absence of cascadingeffects. As pointed out by our interviewees, the rapid recovery of marketsafter initial losses provides a positive evaluation of the robustness of thesystem.

2. Cascading effects can occur again, as our interviewees remarked.However, avoiding cascading or limiting its effects is a question of systemdesign. It might be a very difficult objective to achieve with regulation.


One area of consensus on the need to regulate was on sponsored access.Sponsored (or naked) access gives trading firms using brokers’ licenses unfetteredaccess to stock markets. The Boston-based research firm Aite estimates that by2009 38% of all U.S. stock trading was done by firms using sponsored access tothe markets. The fear is that naked access — typically without (adequate) validationof margins — via direct market access may create strong short-term pricemovements up or down and liquidity crashes.

Professor Hautsch comments, “The problem is not just HFT or direct marketaccess (DMA) but a combination of this together with high leverage, stop orders,naked access, etc. But this does not product bubbles. In normal times, naked accessis not a problem but in non normal times, if all the effects come together, it canproduce a cascading effect. What is missing is a warning system.”

Most sources expect the SEC to act soon on restricting naked access.

H. Who Profits from HFT?

As to who profits from HFT, a first answer, of course, is that HFTers profitfrom HFT. Early estimates by the Tabb Group put HFT profits in the U.S. equitymarkets for 2008 at $21 billion, but the figure was subsequently revised downwardto $7–9 billion. Perhaps coincidentally, the earlier figure is what Kearns et al. (2010)estimated to be the maximum that an omniscient HFTer could earn on the U.S.equity markets. Nevertheless, it was reported that Citadel realized a $1 billion profitfrom HFT in 2007.

If the $7–9 billion estimated profits for HFT is close to reality, global profitopportunities on U.S. equity markets appear to be relatively small, but this numbershould not be surprising: Ultimately, HFT exploits small inefficiencies left aftermajor trends have been exploited. HFT requires very liquid markets. Irene Aldridge,managing partner of Able Alpha Trading LTD, a proprietary firm specializing inHFT, writes that HFT is not profitable in illiquid markets (2010a).

There is some expectation that HFT will be less profitable in the future, atleast in U.S. equity markets. Professor Angel remarks:

Basic statistical arbitrage trading strategy is simple, straight forward, so itis a cut-throat commodity business. To survive, you must be a low-costproducer and do it in scale. There is a lot of competition out there asanyone can buy a computer — they are fairly cheap. The intensecompetition has pushed margins down to almost zero. HFT will not goaway but we will see a shake-out of the less efficient, less intelligentplayers.

As U.S. equity markets become more efficient thanks to tick-by-tick HFTstrategies, sources expect that the diminished returns will see HFTers looking forother sources of profits, including the extension to other asset classes, options markets,and dark space.

Is HFT a zero-sum game in which the HFTers profits are gained at the expenseof other, more slow-moving traders? On her web site Aldridge (2010b) writes,


“While no institution thoroughly tracks the performance of high-frequency funds,colloquial evidence suggests that the majority of high-frequency managers deliveredpositive returns in 2008, while 70% of low-frequency practitioners lost money,according to The New York Times.”

Others suggested that HFTers may have taken the place and profits of otherplayers, such as the market-makers and investment banks. Professor Hendershottcomments, “It is possible that HFT firms are not causing a change in the amount oftrading profit but are taking the profit for themselves. For example, market-makersand banks used to make about $5 billion a year and now this figure is zero or closeto zero.”

The exchanges themselves stand to raise transactional and other revenues asthey gear up to support HFTers with high-speed computers and communicationsand co-location facilities. A source at a major North American exchange comments,“Co-location is a very strong source of revenues, customer loyalty, and stickiness.”But the revenues come at a cost: The exchanges are beefing up their investment intechnology to meet the needs of HFTers.

It is enormously expensive for an exchange to support HFT. Exchanges needto constantly upgrade their architecture to process more messaging. According toindustry sources, it is not uncommon for HFTers to send more than one millionmessages a day and trade only a few contracts. One source comments:

From a technological point of view what is needed is having the requiredrobustness, constantly upgrading from one gigabyte to 10 gigabyte lines,more and more powerful servers, faster speeds, next generation ofcomputers. But next generation architecture is more and more expensive.We are moving towards software to eliminate latency in the computerreading the software code. Software-on-a-chip servers are priced at$100,000 versus $5,000–7,000 for today’s servers. Today we are processingorders at 500 microseconds but racing to do so at single-digit microseconds.

The race for speed has also benefited technology suppliers. One North Americansource observes, “We have seen a proliferation of technology vendors — hardware,software, middlewear, smart order systems, security… The number of technologysuppliers around has tripled over the last 12–18 months.”

Sources from the exchanges also identified benefits for firms listed on theexchange. As mentioned above, at least one exchange evaluates that the activity ofHFTers has brought more investors to the exchange’s listed firms, thereby increasingtheir access to capital and reducing its cost.

Nevertheless, there is concern that the activity of HFTers is concentrated on asmall number of stocks. A representative from a U.S. exchange observes, “Wehave seen a greater concentration [of trades] in the last two years than in the last10 years. It is very dangerous for an exchange when there is so much interest infew names, when all investments concentrated around a few names. We loseflexibility.”

For the investor at large, retail, or institutional, the benefits are not so clear.


While most sources believe that the cost of trading and bid-ask spreads have beenreduced by the activity of HFTers, there is to our knowledge no study that factorsin the cost of exchange infrastructure needed to service HFTers and how this costaffects the total price of trading. Professor Hendershott comments:

A most legitimate concern outside of manipulation is the over investmentin technology, for example, end users of assets as Vanguard, Fidelity wantto find each other and trade directly. The question is: Is the system suchthat whatever the end user does, he/she finds a HFTer on the other sideof the trade? So instead of selling to another end user, the investor sells toan HFTer which in turn sells to another end user. This would be a badthing as trading would become more costly and, normally, a buy/selltransaction should be mutual. …HFTers takes some slice; we can try toget around this with dark pools, for example, a call-auction that occursonce a day. It would reduce the role of the HFTers.

IV. CONCLUSION

In this paper, we analyzed high-frequency trading (HFT) and its econometricfoundation based on high-frequency data. From this analysis it is possible to arguethat HFT is a natural evolution of the trading process, enabled by advances incomputer and communications technology and a high-frequency flow of trades dueto algorithmic trading by long-term investors. High-frequency traders (HFTers)employ computerized algorithms and fast computers and communications channelsto exploit this “raw material.”

Empirical analysis has shown that the presence of HFTers has improved marketquality in terms of lowering the cost of trading, adding liquidity, and reducing thebid-ask spreads. This improvement in market quality comes at a cost as HFTersmake a profit, albeit not a very large profit, as a percentage of trading volume.

Given the short-time nature of HFT and the fact that positions are typically notcarried overnight, the potential for market manipulation and for the creation ofbubbles and other nefarious market effects seems to be modest. The problemsposed by HFT are more of the domain of model or system breakdown or cascading(typically downward) price movements as HFTers withdraw liquidity from themarkets. The former poses a challenge of the design of electronic trading facilities.As for the second, solutions have been proposed including slowing down orinterrupting the trading process or changing the trading mechanism.

References

Aït-Sahalia, Y. and Mykland, P.A., 2003, The Effects of Random and DiscreteSampling When Estimating Continuous-Time Diffusions. Econometrica, 71,483–549.

Aït-Sahalia, Y., Mykland, P., and Zhang, L., 2005, How Often To Sample AContinuous-Time Process In The Presence Of Market Microstructure Noise.Review of Financial Studies, 18, 351-416.


Alridge, I., 2010a, High-Frequency Trading: A Practical Guide to AlgorithmicStrategies and Trading Systems (John Wiley & Sons, Inc., Hoboken, NJ).

Alridge, I., 2010b, How Profitable Are High-Frequency Trading Strategies?.

Andersen, T.G., Bollerslev, T., Diebold, F.X., and Labys, P., 2001, The Distributionof Exchange Rate Realized Volatility. Journal of the American StatisticalAssociation, 96, 42–55.

Andersen, T.G., Bollerslev, T., Diebold, F.X., and Labys, P., 2003, Modeling andForecasting Realized Volatility. Econometrica, 71, 579–625.

Andersen, T.G., Bollerslev, T., and Meddahi, N., 2002, Correcting the Errors: ANote on Volatility Forecast Evaluation Based on High-Frequency Data andRealized Volatilities. Working paper, University of Montreal.

Angel, J., Harris, L. and Spatt, C.S., 2010, Equity Trading in the 21st Century. Workingpaper FBE 09-USC, Marshall School of Business.

Bandi, F.M., and Phillips, P.C.B., 2003, Fully Nonparametric Estimation of ScalarDiffusion Models. Econometrica, 71, 241–283.

Bandi, F.M., and Russell, J.R., 2006, Separating Microstructure Noise from Volatility.Journal of Financial Economics, 79, 655-692.

Bandi, F.M. and Russell, J.R., 2008, Microstructure Noise, Realized Variance, andOptimal Sampling. Review of Economic Studies, 75, 339-369.

Bandi, F.M., Russell, J.R., and Zhu, Y., 2008. Using High-Frequency Data in DynamicPortfolio Choice. Econometric Reviews, 27, 163-198.

Barndorff-Nielsen, O.E. and Shephard, N., 2002a, Econometric Analysis of RealizedVolatility and its Use in Estimating Stochastic Volatility Models. Journal of theRoyal Statistical Society B, 64, 253-280.

Barndoff-Nielsen, O.E. and Shephard, N., 2002b, Estimating Quadratic VariationUsing Realized Variance. Journal of Applied Econometrics 17, 457-477.

Barndoff-Nielsen, O.E. and Shephard, N., 2004, Econometric Analysis of RealisedCovariation: High Frequency Based Covariance, Regression and Correlationin Financial Economics. Econometrica, 72, 885-925.

Bauwens, L. and Giot, P., 2001, Econometric Modelling of Stock Market IntradayActivity (Kluwer Academic Publishers, Dordrecht).

Bauwens, L. and Veredas, D., 2004, The Stochastic Conditional Duration Model: ALatent Variable Model for the Analysis of Financial Durations. Journal ofEconometrics, 119, 381-412.

Bauwens, L. and Hautsch, N., 2006a, Modelling Financial High Frequency DataUsing Point Processes. Discussion paper 2006-39, Catholic University ofLouvain.

Bauwens, L. and Hautsch, N., 2006b, Stochastic Conditional Intensity Processes.Journal of Financial Econometrics, 4, 450-493.

Bertrand, E., 2009, Technology Song and Dance. Presentation at Union of ArabStock Exchanges Conference, Beirut, NYSE Technologies, November.


Bessembinder, H., 2003, Trade Execution Costs and Market Quality afterDecimalization. Journal of Financial and Quantitative Analysis, 38, 747-777.

Boehmer, E., Grammig, J., and Theissen, E., 2006, Estimating the Probability ofInformed Trading: Does Trade Misclassification Matter? Journal of FinancialMarkets, 10, 26-47.

Brogaard, J.A., 2010, High Frequency Trading and its Impact on Market Quality.Working paper, Kellogg School of Management, Northtwestern UniversitySchool of Law.

Brownlees, C.T. and Gallo, G.M., 2006. Financial Econometric Analysis at

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Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas*[email protected]. Caroline Jonas...

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